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OPEN Using dense seismo‑acoustic network to provide timely warning of the 2019 paroxysmal Stromboli eruptions A. Le Pichon1*, C. Pilger2, L. Ceranna2, E. Marchetti3, G. Lacanna3, V. Souty1, J. Vergoz1, C. Listowski1, B. Hernandez1, G. Mazet‑Roux1, A. Dupont1 & P. Hereil4

Stromboli Volcano is well known for its persistent explosive activity. On July 3rd and August 28th 2019, two paroxysmal explosions occurred, generating an eruptive column that quickly rose up to 5 km above sea level. Both events were detected by advanced local monitoring networks operated by Istituto Nazionale di Geofsica e Vulcanologia (INGV) and Laboratorio di Geofsica Sperimentale of the University of Firenze (LGS-UNIFI). Signals were also recorded by the Italian national seismic network at a range of hundreds of kilometres and by infrasonic arrays up to distances of 3700 km. Using state- of-the-art propagation modeling, we identify the various seismic and infrasound phases that are used for precise timing of the eruptions. We highlight the advantage of dense regional seismo-acoustic networks to enhance volcanic signal detection in poorly monitored regions, to provide timely warning of eruptions and reliable source amplitude estimate to Volcanic Ash Advisory Centres (VAAC).

Located in the Aeolian Islands, in Southern Italy, the Stromboli volcano (38.789N 15.213E, 920 m) is known worldwide for its persistent explosive activity of mild intensity from its open vent summit craters. Its ordinary explosive activity, repeating frequently at a rate of ~ 13 explosions/hour1, erupts scoria and ash up to a height of ~ 100–200 m above the craters, with ejecta fallout typically confned a circular crater of about 350 m diameter. Tis activity has been extensively studied with multiple geophysical observations, spanning from ground deformation and seismicity 2–5, infrasound6,7, infrared thermometry 8,9, doppler radar 10 and videogrammetry 11,12. Te ordinary activity at Stromboli is occasionally punctuated by major explosions and paroxysms13,14. Paroxysms represent the largest-scale historical explosive events capable of generating convection plumes up to a height of 10 km and ejecting meter-sized blocks up to distances of 2 km from the vents reaching settled areas of Stromboli island. Te catalog of paroxysms at Stromboli starts from 187913. Since then, 23 paroxysms occurred before 2003 and 4 between 2003 and 201915,16. One of the main risks at Stromboli is due to tsunamis, which are able to afect not only the island but the whole coastal regions of southern Italy 14. Caused by landslide or sector collapses, as well as pyroclastic fows entering the sea, at least 8 tsunamis related to Stromboli happened between 1879 and 2003 13,17. On December 2002, a subaerial 11.6 Mm 3 and submarine 9.5 Mm 3 landslide at Stromboli 18,19 triggered a tsunami wave that locally reached a height of 10 m, impacted the other Aeolian islands, and reached coastal regions of Southern Italy 17,20. Another risk associated with explosive eruptions is related to the emission of volcanic ash in the atmosphere. During an eruption, volcanic ash can reach and exceed the cruising altitudes of aeroplanes within minutes and spread over vast geographical areas within a few days. Encounters with volcanic ash may result in several prob- lems such as malfunction or failure of engines. Afer some dramatic ash encounters by airplanes in the 1980’s, International Civil Aviation Organization (ICAO) has set up the International Airways Volcano Watch (IAVW). IAVW is based on 9 Volcanic Ash Advisory Centres (VAACs) designated by ICAO to provide near-real-time information on the largest possible number of volcanic events that afect aviation. Stromboli is located in the area of responsibility of the Toulouse VAAC, which includes a large part of Europe and Africa. In the IAVW chain of information, state volcano observatories play an essential role in providing to the VAACs near real time information on volcano activity from their monitoring networks.

1CEA/DAM/DIF, 91297 Arpajon, France. 2BGR, B4.3, 30655 Hannover, Germany. 3Department of Earth Sciences, University of Firenze, 50121 Firenze, Italy. 4Meteo France, Toulouse VAAC, 31057 Toulouse, France. *email: [email protected]

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Unexpected changes in explosion intensity at Stromboli are due to the dominant role of shallow conduit processes triggering paroxysmal activity 21. On July 3rd and August 28th 2019, the volcano produced such paroxysms, followed by intense explosive and intermittent efusive activity. Visual observations and the analysis of the fall deposits allowed to characterize pyroclasts and reconstruct ballistic exit velocities of up to 160 m/s22. Paroxysms are driven by deep magma batches 23 that eventually fragment in the shallow system producing the observed eruptive columns24,25. Short-term precursors of the July 3rd and August 28th 2019 paroxysms were identifed26. Te 2019 episodes consisted of large volcanic explosions, a few seconds apart, from diferent summit craters. Te released eruptive column reached a height of ~ 5 km and produced a fall-out of lithic blocks, decimeter-sized scorias and ash afecting the summit areas as well as the inhabited settlements of the island. Te collapse of the eruptive columns produced pyroclastic fows along the Sciara del Fuoco that entered the sea and triggered local tsunamis that reached wave heights of 1 m27. Following the July 3rd explosions, the eruptive plume rose up the summit. Te explosion was monitored in real time by two networks deployed and operated on the island by Laboratorio di Geofsica Sperimentale of the University of Florence (LGS-UNIFI)28 and Istituto Nazionale di Geofsica e Vulcanologia (INGV)29. With this event, INGV rapidly issued a volcano activity warning 30 min afer the eruption through its 24/7 operating system (https://www. ct. ingv. it/ index. php/ monit oragg io-e- sorve glian za/ prodo tti- del- monit oragg io/ comun icati- attivita-vulcanica). Te Toulouse VAAC, then issued a Volcanic Ash Advisory (VAA) to the ICAO accounting for the presence of a volcanic ash cloud, drifing northerly. Tis VAA was based on satellite observations of the volcanic ash cloud. On August 28th, short-time ground deformation precursors allowed an alert to be issued 5 min before the onset of the eruption 30 and a Volcano Observatory Notice for Aviation (VONA) was sent by INGV about 30 min afer the paroxysmal explosion, alerting for the presence of an ash plume rising up to 5 km above sea level (http:// www.ct.ingv.it/index.php/monitoraggio-e-sorveglianza/prodotti-del-monitoraggio/comunicati-vona). A VAA was then issued by Toulouse VAAC announcing the presence of a drifing ash cloud in the vicinity of the volcano. Infrasound observations can provide additional information about active volcanic processes 31. Te 2019 paroxysms were recorded at hundreds of kilometres across the permanent Italian seismological network operated by INGV, and in the far-feld up to ~ 3700 km, by infrasound stations part of the International Monitoring System (IMS) completed by national arrays. At regional scales (e.g. beyond the frst stratospheric returns at 150–200 km), combining observations from seismo-acoustic arrays allows improving operation monitoring methods to discriminate between natural and anthropogenic phenomena32. Johnson and Malone33 demonstrated that the source chronology and the timing of eruptions can successfully be calculated from ground-coupled airblasts observed at seismic stations. Analyzing records of dense seismic networks such as the transportable USArray34 or the European AlpArray35 provided unprecedented spatial detail of the infrasound ground footprint, allowing the detection and localization of both natural and man-made events with great precision. Using state-of-the-art modeling, the new era of massive datasets ofers an opportunity to examine the propagation of infrasound wavefeld across regional seismic network in more detail than previously possible and invert source information of a volcanic eruption. In this study, we identify infrasound radiation from the 2019 eruptions recorded at both near- and far-feld infrasound arrays as well as by seismic stations distributed across Italy. We show how far-feld measurements are capable for providing timely warning to VAACs and estimating the source amplitude for remote volcanoes where local instrumentation is missing. Results Infrasound observations. Te increased number of operating IMS stations and the establishment of regional infrasonic arrays demonstrate unprecedented potential of such an enhanced network in terms of detection capability, in particular for remote volcano monitoring36,37. In addition, national seismoacoustic monitoring systems have been developed in central Europe over several decades to fll a gap in the global IMS network38. Nowadays, the detection and location capabilities of combined networks ofer a unique opportunity to investigate methods for discriminating between natural and artifcial acoustic sources, as well as to better understand seismoacoustic coupling mechanisms at the Earth’s interface39,40. Figure 1 shows the relevant infrasound network surrounding Stromboli over the Euro-Mediteranean region. At the time of the July 3rd and August 28th eruptions, easterly stratospheric wind fow prevailed at 30–60 km altitude and favored westward stratospheric propagation. Infrasound records at four IMS stations (IS26, IS42, IS37, IS48) and three national infrasound arrays (AMT, OHP, CEA) are analyzed. Table S1 highlights the detections for the July and August eruptions in short to medium distances (AMT: 543 km; IS48: 618 km; OHP: 977 km; IS26: 1124 km; CEA: 1509 km), as well as at long ranges (IS37: 3379 km; IS42: 3711 km), covering western (IS48, IS42) to northern (IS26, IS37) directions. Figure S1 presents an example of infrasound detection at the IMS station IS48 for the July eruption. Wave parameters are calculated using the progressive multi-channel correlation method (PMCC) in the 0.1–4 Hz frequency band. Long lasting coherent waves are detected from 15:17 to 15:40 UTC. Te increase with time of the apparent velocity (from 360 m/s to 380 m/s) indicates an increase of the ray turning heights at stratospheric altitudes. Te frequency content of the detections is consistent with the low frequency (< 1 Hz) of infrasound produced by the paroxysm, that was followed by an intense spattering and explosive activity characterized by the higher frequency component (2–5 Hz) observed afer 15:25 in the coda of the signals. Table S1 summarizes the onset time, duration, back-azimuth, apparent velocity, frequency range and peak- to-peak amplitude of the detections. All arrivals are stratospheric, with average celerities ranging from 284 m/s to 312 m/s. Only the detection at IS37 in August might be thermospheric with a celerity of 267 m/s and arriving about 20 min later than would be expected for purely a stratospheric duct. Back-azimuth deviations from the

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Figure 1. Attenuation maps derived from range dependent PE simulations at 1 Hz for the July 3rd (lef) and August 28th (right) eruptions. Color-coded backgrounds represent the surface attenuation predicted by the PE model. Te colored station markers represent attenuation of the array-observed amplitudes compared to a reference source amplitude at 1 km of 1510 Pa (July) and 466 Pa (August). For the sake of visibility, the northern most station IS37 is not included in the graphs. Table S2 provides details of the observed and modeled attenuation at all infrasound stations. Te stratospheric wind feld at 50 km altitude is represented by black arrows (50 m/s reference provided in the lower lef corner). Te map was generated using Matlab Mapping Toolbox Version 4.6 (https://www. mathw orks. com/ produ cts ).

Figure 2. Raw infrasound pressure recorded at Stromboli for the July (top) and August (bottom) events reduced at 1 km from the source (black curve). Peak amplitudes of the frst arrival reduce down to ~ 1300 and ~ 700 Pa respectively once band-pass fltered in the 0.5–2 Hz frequency band (red curve).

true direction to Stromboli are all within 2°, except in the case of IS37 for the August eruption, which has a 6° deviation and is likely related to higher cross-winds afecting its southward propagation path. Figure 2 shows the raw infrasound pressure recorded at Stromboli by infrasound sensors operated by LGS-UNIFI for the July (a) and August (b) events at a reduced distance of 1 km from the source assuming a spherical geometrical spreading.

Seismic observations. Infrasound waves from the July 3rd and August 28th paroxysmal explosions were also detected by the permanent Italian seismological network up to a range of ~ 700 km. Figure 3 shows the time

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Figure 3. Hodochrons of seismic waveforms recorded at INGV seismic stations up to a distance of 700 km for the July (top, 198 stations) and August (bottom, 154 stations) eruptions. Time is relative to the main explosions (14:45:42 and 10:17:16 for the July and August eruptions, respectively). Te envelopes of band-pass fltered data between 0.5 and 2 Hz are displayed. Lef: distance versus relative time; theoretical arrival times derived from WASP-3D ray tracing simulations with turning heights color coded (in km). For the July eruption, the coherent seismic phases observed at a relative time of about 800 s for distances between 550 and 650 km show an apparent velocity consistent with a seismic phase. Tey are caused by a magnitude 1.8 earthquake that occurred at 16:59:30 UTC 33 km west of Siena, Tuscany (http://terre moti. ingv. it/ event/ 22597 531 ). Middle: time shifed traces using a constant celerity model of 300 m/s. Right: time shifed traces using celerity models derived from WASP-3D simulations.

shifed seismograms according to a fxed celerity and modelled propagation times for stratospheric ducting (hodochrons in Fig. 1). Records exhibiting abnormal noise level likely related to sensor malfunction have been discarded. Time is relative to the origin of the main explosion (14:45:42 and 10:17:14 for the July and August eruptions, respectively) and are calculated from local infrasound records (Fig. 2) corrected for the source-to- receiver propagation time. Aligning the envelopes of band-pass fltered data between 0.5 and 2 Hz using a constant celerity of 300 m/s reveals the signature of stratospherically ducted air-to-ground phases up to a propagation range of ~ 600 km34. In order to recover the source-time function of the eruption sequence from remote observations, a detailed analysis of the seismic records at stations located up to a distance of ~ 200 km from Stromboli is carried out. Figure S2 presents the seismic records, band-pass fltered between 2 and 8 Hz,. Out of the 38 available stations, impulsive signals are observed at four stations (MILZ, IFIL, MSRU, USI) with arrival times consistent with seismi- cally coupled underwater acoustic waves (T-waves)41. Tese signals are associated with a seismic precursor which occurred at 14:44:44 UTC, about 1 min before the frst explosion. Te observed signals are not compressional P-waves usually generated by explosive events but hydroacoustic waves travelling at a velocity of approximately 1500 m/s, converted to seismic waves on the fanks of an island or on the continental coastal shelf. Te travel times of the onset times of phases marked in Figure S2 is consistent with the expected velocity of T-waves.

Long‑range propagation modelling. For the July and August eruptions, 2D parabolic equation (PE) simulations clearly highlight several stratospheric bounces to the west with reduced attenuation (Fig. 1) and are in agreement with the summer conditions of the predominant westward stratospheric wind. Te frst fve to ten ground returns of stratospheric waves are visible as concentric rings of reduced amplitude arrivals to the west of Stromboli reaching arrays AMT, IS48 and OHP. Tese stations are all within 1000 km of Stromboli and are in a range of azimuths where stratospheric returns are modeled with attenuation values between 50 and 65 dB. At greater distances, stations CEA, IS26 and IS42 capture stratospheric phases with higher attenuation values

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between 65 and 95 dB, while IS37 located at 3379 km to the edge of stratospheric ducting arrivals has attenuation between 100 and 110 dB. Reference source amplitudes ranging from 1 Pa to 10 kPa with 1 Pa steps are applied to defne the respective observed attenuations at the diferent stations. Tis reference is estimated by applying a least square ft between the modeled and observed attenuation values at seven stations (Table S2). Te minimized quadratic diference occurs for a source amplitude of 1510 Pa on July 3rd and 466 Pa on August 28th with standard errors of 8 dB and 14 dB respectively when considering all observations. Te converted station attenuations deduced from the latter results are in the range of 50 to 65 dB for AMT, IS48 and OHP, between 65 and 85 dB for CEA, IS26 and IS42 (excluding the low amplitude station observation of IS42 in August) and 90 to 115 dB for IS37. Tis method of deriving source signal intensity independently from near-source observations yields results consistent with near-feld measurements peaking at ~ 1300 and ~ 700 Pa respectively once band-pass fltered in the 0.5–2 Hz frequency band of analysis of long range infrasound data (Fig. 2). Figure 3 presents the hodochrons of the seismic waveforms recorded at INGV seismic stations up to a distance of 700 km from Stromboli for the July and August eruptions. Superimposed on the lef panels are theoretical arrival times of direct (up to ~ 80 km, celerity of 340 m/s) and stratospheric phases (frst branch ranging from ~ 200 km to ~ 400 km and second branch ranging from ~ 400 km to ~ 650 km; celerities between 270 m/s and 305 m/s). At almost all stations, the maximum of the signal amplitude coincides with the frst and second stratospheric branches with ray turning heights ranging between 35 and 50 km. Te summer atmospheric conditions of July 3rd and August 28th are comparable. Te mean time residuals (mean of the diference between the observed and modeled propagation times) reduce from 20 ± 4 s when using a constant celerity of 300 m/s to 5 ± 2 s when accounting for a variable model-based celerity. Figure 4 compares the recorded and modeled infrasound waveforms obtained from normal mode simulations42 of the wave equation for the July and August eruptions. For each station, range-dependent efective sound speed profles are considered. Te source time function used to model synthetic waveforms is the zero-phase Ricker wavelet with a dominant frequency of 1 Hz. Overall, a good agreement between the observed and predicted arrival times and signal duration is observed. Considering the onset times of dominant arrivals (one per station), the mean arrival time residual is 4.8 ± 0.5 s. Beyond 500 km, dominant arrivals switch from the frst to the second stratospheric branch for both events. In the observations, the frst stratospheric branch does not extend beyond ~ 500 km, as predicted for the August eruption. For the July eruption, the propagation simulation extends the frst stratospheric branch up to ~ 600 km; this efect can result from inaccurate atmospheric specifcations43 or unrealistic gravity wave felds difracting acoustic energy into the geometric shadow zone 44.

Location accuracy. Figure 5 shows the time residuals (SSE) for both July and August eruptions considering a constant celerity of 300 m/s and travel times derived from 3D ray tracing simulations. No assumption is made on the event location. Te search region extends from 36 to 44 N and 10E to 20E with a grid resolution of 0.5 km. Te travel times are calculated over a time period of 2 min centered on the origin time of the paroxysmal eruptions with a time step of 1 s (Figure S2). Te minimum SSE is calculated over the studied region (blue curves), from which the distance misft between the candidate source point and Stromboli is calculated (red curves). Using a constant celerity of 300 m/s, the minimum of SSE is reached at 14:45:48 UTC on July 3rd and 10:17:46 UTC on August 28th, with corresponding errors of 6 s and 32 s compared with the true origin time. When considering modeled celerity values using atmospheric models from the European Centre for Medium- Range Weather Forecasts (ECMWF IFS cycle 38r2, http://www.ecmwf.int), the origin time error reduces to ~ 2 s (14:45:40) in July and ~ 3 s (10:17:13) in August, and the corresponding location error decreases from 1.6 km to 1.1 km in July, and 3.7 km to 1.3 km in August. Figure 6 presents the geographical distribution of the time residuals for the July and August eruptions. Time residuals are calculated using the origin time given by the minimum of SSE (Fig. 5, solid blue curve). Due to the geographical distribution of the stations, the residual contours are elongated east–west and location uncertainty is greater in this orientation. For comparison, the locations obtained using back-azimuths from seven infrasound arrays only are indicated by the red crosses. Te red ellipses show the 95% confdence location using wind (ECMWF IFS) corrected back-azimuths (Table S1) and a measurement uncertainty of 1° appropriate for arrays of kilometre-scale45. When considering locations derived from infrasound arrays only, the source is located 31 km and 16 km north of Stromboli for the July and August eruptions, respectively.

Notifcation of volcanic activity. During the last decade, the deployment of infrasound stations at local, regional and global scales has signifcantly increased the potential of infrasound measurements to mitigate volcanic hazards46. In particular, it was demonstrated that infrasound can play a key role in supporting warning systems by notifying, in real-time, the onset of explosive eruptions47, thus reducing the risk of aircrafs encoun- tering volcanic ash in poorly monitored regions. Te amplitude of infrasound detections associated with the July and August eruptions is corrected for propagation efect along each source-to-receiver pathto infer the source amplitude at a reference distance of 1 km from the crater48. Te source amplitude is then multiplied by the normalized number of detections per minute, which refects the time persistency of the signals recorded at the array. Applying the procedure described by Ulivieri et al.49 and Ripepe et al.47, the occurrence of signifcant activity at Stromboli is estimated from remote infrasound observations. Infrasound detections at all arrays are fltered according to the true back-azimuth to Stromboli (± 10°), band-pass fltered from 0.5 to 2 Hz, and the mean amplitude (P) is calculated in a sliding window of 20 min. Te time persistency of the signals is quantifed by the number of detection per minutes (Ndt), normalized to 60. Te mean amplitude (P) is corrected for propagation efect along each source-to-receiver paths in order to infer the source amplitude at a reference distance of 1 km

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Figure 4. Comparison between the recorded (lef panels) and the modeled (right panels) waveforms at seismic stations for July (top panels) and August (bottom panels) eruptions. Only stations with clear signals (SNR > 10 dB) are displayed (50 and 38 stations for the July and August eruptions, respectively). Station names, distances and azimuths are specifed to the lef. Waveforms are time-shifed using a constant celerity of 300 m/s. Vertical red bars are onset times of dominant arrival at each station used for the localization (Figs. 4 and 5), performed on the recorded waveforms band-pass fltered between 0.5 and 2 Hz. To ease the comparison between data and simulation, picks are reported on the modeled waveforms (right). A good agreement beween the predicted and observed arrival times, but also shapes and durations is observed.

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Figure 5. Sum of squared errors (SSE) (blue curves) and location errors (red curves) for the July (lef) and August (right) eruptions as a function of trial origin times. Dashed and solid lines correspond to a constant celerity (300 m/s) and azimuthal/range dependent celerity models derived from WASP-3D ray tracing simulations, respectively.

Figure 6. Geographical distribution of the time residuals for the July (lef) and August (right) eruptions using the origin time given by the minimum of SSE. Grey curves are isocontours of SSE. White inverted triangles are selected seismic stations where clear signals from the eruptions (SNR > 10 dB) were observed (50 and 38 stations for the July and August eruptions, respectively). Te red crosses indicate the centroid of cross-bearing location considering wind-corrected back-azimuths at stations IS26, IS37, IS42, IS48, AMT, OHP and CEA. Te red ellipses show the 95% confdence. Te map was generated using Matlab Mapping Toolbox Version 4.6 (https:// www.mathw orks. com/ produ cts ).

from the crater (Ps). Te source pressure and the signal persistency are then combined to derive the infrasound parameter (IP = Ps*Ndt) that is used to identify signifcant ongoing volcanic activity47,49. A notifcation is obtained when IP exceeds a threshold set to 60 over a period of at least 20 min50. Figure 7 shows the IP variations at stations AMT, IS48, OHP, and IS26. IP values exceeding the threshold of 60 are highligted.. By applying such an approach, notifcations could have been delivered up to a distance of 1124 km (IS26) and 618 km (IS48) for the July and August events, respectively. For information purpose, the July 3rd notifcation based on infrasound observations at the closest IMS array in Tunisia would have preceded in the best case the VAA alert issued at 17:00 UTC by 105 min. On August 28th, a VONA was sent by INGV at 10:48 UTC, 31 min afer the eruption, allowing a VAA to be issued by Toulouse VAAC at 10:56 UTC. In this case, the frst infrasound based notifcation using records at IS48, would have been possible at 11:10 UTC. It should be noted that no location can be computed using a notifcation based on a detection at single array, as opposed to more detailed source information derived from the infrasound wavefeld analysis across a dense network. Te level of confdence of such notifcation should therefore account for the station detection capability and its sensitivity to local environmental noise. Te added value of regional seismic network to contribute to an alert system in poorly monitored regions would require further evaluation and benchmark testing which are out of the scope of this paper.

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Figure 7. IP derived from infrasound detections at several stations for the July 3rd (a) and August 28th, 2019 (b) paroxysms at Stromboli. Te vertical red line identifes the time of issuance of the VAA from Toulouse VAAC, while the pink line indicates the 300 m/s travel-time typical of stratospheric arrivals. Te onset time of increased volcanic activity, based on the IP values exceeding the threshold of 60 for at least 20 min at each array, is shown by the red arrows. Such notifcation would have been possible at AMT, IS48 and IS26 for the July event, and at IS48 for the August event.

Discussion Te 2019 paroxysmal eruptions of Stromboli were clearly detected by IMS infrasound stations up to a distance of 3711 km. In addition to the IMS network, signals were also recorded by the national seismological network across Italy. Te infrasound signature of the eruptions as measured by infrasound and seismic sensors has been modeled at local and regional distances (direct/tropospheric versus stratospheric returns). Te amount and variety of observed infrasound phases represents a unique dataset for statistically evaluating atmospheric models, numerical propagation modeling and localization methods. At distance of about 170 km from Stromboli, transient signals were observed at four seismic stations (MILZ, IFIL, MSRU, USI) with arrival times consistent with T-waves. Te timing of the T-waves is not consistent with the paroxysmal explosion but rather to a shallow volcano-tectonic earthquake reported by Giudicepietro et al.26 which occurred at 14:44 UTC, one minute before the July 3rd eruption. Te lack of T-wave observations at other stations is explained by a masking efect (see map on Figure S3). A modeled estimate of the ground return footprint of stratospheric arrivals is recovered using 2D PE and ray- tracing simulations, as well as normal mode simulations. Te model-predicted and array-observed infrasound attenuation ranges correspond to values within ± 10 dB for July and August (Table S2). Te average deviation in dB between model and observation are 3.4 dB for the July eruption and 8.7 dB for the August eruption. Te higher accuracy of the modeling on July 3rd is explained by a more stable and favorable ducting condition, lowering uncertainty in modeling the amplitude 51. In August, the uncertainty between model prediction and observation is especially high at IS26, as the station is located outside of the modeled stratospheric cone. By minimizing the quadratic diference between the observed and predicted attenuation, a source amplitude of 1510 Pa on July 3rd and 466 Pa on August 28th is inferred. Tis independently derived source amplitude is consistent with near feld observations when modeling long-range propagation at 1 Hz and band-pass fltering records around the dominant frequency of the signal (0.5–2 Hz) (Fig. 2). Using only IMS infrasound detections, the cross-bearing location shows errors up to ~ 30 km. Using the arrival times of air-to-ground coupled waves and celerity models derived from 3D ray-tracing simulations reduce the origin time error down to ~ 3 s. Tese results underline the beneft of integrating local and regional infrasound networks as well as seismic networks into the global IMS network for improving location and discrimination methods which are used as efective tools for the CTBT verifcation regime. Tis study also highlights the added value of exploiting the synergy between complementary networks to develop efcient multi-technology monitoring systems for disaster prevention or mitigation52. It should be emphasized that volcanic signals recorded by remote seismo-acoustic monitoring systems are less valuable due to reduced signal-to-noise ratio and propagation time (e.g. latency of ~ 15 min at 300 km). Furthermore, while infrasound is recorded on seismic stations up to distances of 700 km, the seismic signal produced by the explosion is limited to stations located within ~ 250 km, thus limiting the use of seismic waves only to local and regional distances. However, as infrasound propagate downwind with reduced attenuation, recent advances in network performance modeling allows optimizing network layout in order to best detect and characterize volcanoes 53. Te reverse time migration method, which was successfully implemented by Walker et al.54, would be highly

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benefcial to automatically detect infrasonic signals registered by a dense seismo-acoustic network and locate the source. Compared with detection at single infrasound array, such an approach increases the confdence level of the notifcation by discarding false events along the direction of the targeted volcano. Following the detection stage, propagation modeling using a realistic description of the atmosphere would provide a precise source location reducing false alarms associated with detection timing of the eruptions and reliable source amplitude estimate. Te real-time reliability of the reverse time migration method would require further statistical performance testing to defne acceptable detection thresholds (e.g. SNR, number of detections) to be used under realistic operating conditions. Within recent years, the development of cost-efective acoustic sensors ofers an opportunity to examine the propagation of infrasound wavefelds, in high resolution, across a dense scalable network55. Traditional methods used to monitor volcanoes have inherent drawbacks for volcanic hazard assessment (e.g. local monitoring sensors are vulnerable during large volcanic eruptions and ash plumes below cloud cover are difcult to detect using satellite remote sensing). Te infrasound technology ofers an alternative tool to mitigate volcanic hazards by providing not only the timing of the eruption chronology by also estimate of the plume height which is a key input parameter for running ash dispersion models. Such technological advances, associated with improved processing and propagation modeling methods, share the advantages of being non-invasive and capable of exploring wide areas of investigation. Tis geophysical exploration technique is particularly benefcial to monitor volcanic regions with little infrastructure, being not limited by feld accessibility. Te efectiveness of such method has been demonstrated at propagation ranges of thousands of kilometres through eruption case studies in Southeast Asia where there are around 750 active or potentially active volcanoes 56. It is expected that pursuing such evaluation would contribute to improving methods for natural hazards monitoring from the perspective of building a timely warning system to VAACs in poorly monitored regions. Methods Data processing. Te PMCC was applied to the raw pressure sampled at 20 Hz to detect coherent infrasound signals within the background noise and estimate the wave front parameters 57. Te time and frequency window parameters for PMCC processing were set using 1/3-octave band scheme in the 0.1–5.0 Hz band to facilitate detection of broadband signals. Window time durations were set to vary linearly with the period, with a 90% overlap. Such log-scale confguration with variable window length improves discrimination between inter- fering signals58. At a sampling rate of 20 Hz, the resolution of the azimuth is about 1° and 5 m/s for the horizontal trace velocity43. To quantitatively determine the optimum source location using the arrival time of air-to-ground coupled waves observed across the Italian seismic network, a grid-search method for a single-source model is implemented. Te optimum location is estimated by calculating the normalized sum squared errors (SSE) of the misft between the observed and predicted arrival times at seismic stations 59.

Propagation modelling. To predict the pressure wave attenuation, infrasound propagation is modeled using a two-dimensional parabolic equation approach (2D PE) up to distances of 4500 km from Stromboli60. Simulations are computed covering the full azimuth range with a step width of 0.1°. Atmospheric variability is taken into account using time-varying atmospheric models. Te used ECMWF IFS analysis products contain gravity waves (GWs) originating from diferent sources such as orography, convection, wind shears, jets and fronts. IFS captures well the synoptic scale meteorology below ~ 30 km altitude. However, activity and interac- tion of GWs with the mean fow are not predicted accurately due to imperfect parameterisations 61, or the lack of fne scale orography leading to underestimated or missing GW activity 62, for instance. Te lack of assimilated observations at stratospheric altitude and a sponge layer starting already in the stratosphere are also responsible for signifcant temperature and wind biases in the middle atmosphere 43. In order to account for unresolved wind perturbations, small scale atmospheric variations from the spectral gravity wave model developed by Gardner et al.63 are added to the ECMWF atmospheric felds. Such empirical corrections signifcantly afect infrasound propagation in the stratopause region where ray-turning heights are quite sensitive to small-scale atmospheric perturbations51. Tis approach was already successfully employed to explain explosion detections through dif- fraction and scattering of acoustic energy into the geometric shadow zone across Europe 44. For identitying the propagation paths of the recorded signals, long-range infrasound propagation is simulated using the windy atmospheric sonic propagation ray theory-based method (WASP-3D) which accounts for the longitudinal variation of the atmospheric model along the propagation paths 64. Te ray canonical variables (slowness vector, position, and propagation time) are numerically solved by linearized hydrodynamic equations in spherical coordinates. Following a shooting procedure, the azimuthal deviations of eigenrays sought between Stromboli and infrasound arrays are calculated. Rays are classifed and labeled depending on their turning heights and number of ground refections before reaching the station. Extracted celerity models and azimuthal deviations are median values among the selected rays. Tis procedure, which is preferable to costly eigenray techniques, yields reliable station-dependent travel times and azimuthal corrections needed for accurate source localization 40. Synthetic waveforms are also calculated at seismic stations where the signal-to-noise of the observed air-to- ground coupled signals allows unambiguous arrival time phase picking. Te full-wave propagation method used is a low order range-dependent propagation model obtained from a normal mode wavelet-based decomposi- tion of atmospheric perturbations 42. Selecting the components leading to the most sensitive eigenvalues yields accurate simulations with signifcantly reduced computational cost.

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Data availability Seismic records were obtained from the national seismic network operated by INGV (http://esm. mi. ingv. it , last accessed August 2020). Te vertical component data of broadband seismic stations were downloaded from the INGV International Federation of Digital Seismograph Networks (FDSN) web services (http://terremoti.ingv. it)65. ECMWF products, including the atmospheric model analysis are available via https://www.ecmwf.int/en/ forecasts/dataset (last accessed August 2020) under CC-BY 4.0 License. Bathymetry and topographic data are from the Shuttle Radar Topography Mission (SRTM30) digital elevation model (DEM) (http://eros.usgs.gov). Te DTK-GPMCC sofware included in the NDC-in-a-Box package designed for infrasound array processing is available upon request. Infrasound records at IMS and national arrays can be found at the BGR data product center (https://produ ktcen ter. bgr. de/ terra Catal og/ Detai lResu lt. do? fleI denti fer= ef5bd 209- a3a1- 44de- b8c6- ec5e7 a0dce76).

Received: 27 November 2020; Accepted: 18 June 2021

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66. Blanc, E. et al. Toward an improved representation of middle atmospheric dynamics thanks to the ARISE project. Surv. Geophys. 39, 171–225. https://doi.org/10.1007/s10712-017-9444-0 (2018). Acknowledgements Te authors are grateful to the CTBT Organization and IMS station operators for guaranteeing the high-quality infrasound data. Te authors are grateful to Maurizio Ripepe for useful discussions. Te authors also thank Samuel Kristofersen for proofreading of the manuscript. Tis study was facilitated by previous research performed within the framework of the ARISE project 66, funded by the European Commission FP7 and Horizon 2020 programmes (Grant agreements 284387 and 653980). Author contributions All of the authors contributed to the manuscript. In detail: A.L.P., C.P., E.M. and V.S. wrote the manuscript and realised the fgures; G.L. analysed local infrasound records; J.V. realised full-wave propagation modeling; C.L. evaluated atmospheric models and carried out sensitivity studies; B.M., G.M.R. and A.D. analysed seismic data from INGV network; P.H. analysed the VAA in comparison to the infrasound detections. All authors reviewed the manuscript.

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